## Abstract

This paper examines the relationship between competition, cost innovation, and x-inefficiency in experimental markets. In the lab, oligopolists make closer-to-optimal cost innovation expenditures than do monopolists, which result in lower x-inefficiency in oligopoly than in monopoly. Oligopolies also increase total surplus relative to monopoly, and consumer surplus makes up a larger portion of total surplus in oligopoly than monopoly. The data illustrate how x-inefficiency affects surplus dynamically and suggest price as a mechanism by which competitive pressure increases cost efficiency.

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## Notes

- 1.
X-inefficiency is defined as the difference between actual and minimum cost of production for a given output (Leibenstein 1978).

- 2.
- 3.
The exchange rate between experimental and U.S. currency was $10.00 experimental dollars to US$1.00.

- 4.
If, over the course of several periods, a subject used his endowment on innovation and did not offset this expenditure with earnings from the Market stage, his cumulative profit fell. If a subject’s cumulative profit dipped below $3.00 during a block, the experimental software only let him purchase as many attempts as he had funds for. His cumulative profit could reach $0.00, but could not go negative. Across all treatments there were only six cases where a subject’s cumulative profit reached $0.00. In each, the subject in question subsequently earned profits in a Market stage and ended the block with a cumulative profit above $0.00.

- 5.
Subjects set their capacity to 8 units 77.5 % of the time, so while the Market stage was a price-capacity game, competition

*de facto*focused on price. Subjects very rarely made capacity choices that, given their marginal cost and chosen price, restricted their sales (and thus their profit). Out of 2220 capacity choices in the data, 104 (4.7 %) were “mistakes” in this sense. 59.6 % of these mistakes occurred in either periods 1 or 2 of Block 1. In Blocks 2 and 3, subjects made capacity mistakes just 2.2 % of the time. - 6.
As in naturally-occurring markets, sellers had incomplete information about demand. Though this added complexity to their decision task, optimal price was a discovery process for subjects in

*all*treatments. - 7.
An alternative motivation is the presence of a barrier to competitive entry (

*Monopoly*), its removal (*Oligopoly*), and eventual reinstatement (*Monopoly*). - 8.
There were two reasons for this differential feedback. First, subjects in the \(n>1\) treatments were given more feedback in monopoly so that their feedback would be constant in both monopoly and oligopoly. Second, it was possible that with more feedback, imitation would induce subjects in the \(n>1\) treatments to attempt more innovation in Block 1 than did ONE subjects. Unreported regressions (available from the author) indicate that this did not occur: There was no significant difference in innovation expenditure across treatments.

- 9.
Though this feature of the design is perhaps unrealistic, subjects were in the dark about competition only during the Innovation stage of period 1. Thereafter they knew exactly how many competitors they faced.

- 10.
- 11.
Formally, for market structure \(j\in \{{\text {monopoly, duopoly, quadopoly}}\}\) and a given block, average profit for cost level \(\overline{s}\) is:

$$\begin{aligned} \pi _j(\overline{s})=\frac{\sum \limits _{t=1}^{10} \sum \limits _{i=1}^{N_j}\mathbb {1}\{s_{it}=\overline{s}\} (p_{it}-s_t)q_{it}}{\sum \limits _{i=1}^{N_j}\mathbb {1}\{s_{it}= \overline{s}\}} \end{aligned}$$where

*i*indexes subjects in market structure*j*, \(N_j\) is the number of subjects in market structure*j*in the block, prices are denoted by*p*, sales by*q*, and \({\mathbb {1}}(\cdot )\) is the indicator function. - 12.
Unreported regressions (available from the author) indicate no significant differences across treatments in Block 1. In Block 3, price was initially lower in TWOREV and FOURREV than in ONE, because subjects in the former treatments were not sure if they were monopolists or oligopolists. They quickly figured out that they were monopolists and raised their prices.

- 13.
6 of the 77 average profit figures that were used to calculate these optimal paths were imputed from linear or polynomial regressions because a few cost levels were never reached in certain market structures.

- 14.
These results are subject to the caveat that independence across periods in the deviation paths is not strictly satisfied.

- 15.
Isaac and Reynolds (1992) also report under-investment in cost innovation in their similar environment.

- 16.
When x-inefficiency is calculated relative to the exogenous cost frontier (optimality is a cost reduction in each period), or relative to the subject with the lowest cost in each treatment (the “best practice firm”), x-inefficiency is significantly lower in oligopoly than monopoly in Block 3.

- 17.
For a notable critique of x-inefficiency theory, see Stigler (1976).

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## Acknowledgments

I am grateful to Mark Isaac, Taylor Jaworski, Stanley Reynolds, Cortney Rodet, and Bart Wilson for helpful comments and discussion and to Philip Brookins and John Jensenius for programming advice. I also thank my dissertation committee and participants at the xs/fs Experimental Reading Group at Florida State and the 2013 Public Choice Society Conference. Finally, I thank two anonymous referees and especially Lawrence White for comments that have greatly improved this paper. Naturally, any errors are my own.

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## Appendix

### Appendix

Note: these are the instructions from FOUR and FOURREV. To maintain neutral language, the monopoly market structure was referred to as ‘multiple’ and quadopoly was referred to as ‘single’.

### Instructions

This is an experiment on economic decision making.

Please __turn off and stow all electronic devices__ (cell phones, computers, tablets, etc.).

Also, please __do not communicate with other subjects__ from now until the end of today’s experiment.

If you have a question at any point during these instructions or during the experiment, please raise your hand and an experimenter will come to your terminal to address your question privately.

For participating in today’s experiment you will receive a show-up fee of $10 plus the amount you earn during the course of the experiment. During the experiment, your earnings (excluding show-up fee) will be designated in experimental dollars ($). At the conclusion of the experiment, experimental dollars will be converted into U.S. dollars (US$) at an exchange rate of $10.00 to US$1.00.

Example: If you earn $80.00 during the experiment, you will be paid US$8.00 at the conclusion of the experiment.

You cannot leave today with less than your US$10.00 show-up fee.

This experiment is composed of 3 **blocks**.

Each block is divided into 10 **periods** and each period is further sub-divided into 2 **stages**.

In other words, this experiment consists of 3 blocks, 10 periods and 60 stages total. At any point during the experiment you can determine the block number, period number, and stage by examining the top of your computer screen.

In each period, you will first participate in an **Innovation stage** and then in a **Market stage**. We will discuss the Market stage first.

### Market Stage

In each Market stage, you will have the opportunity to sell units of a good.

You will have a production cost per unit, or an amount it costs you to produce a single unit. This production cost per unit is constant regardless of how many units you produce.

Example: Say your production cost per unit is $7.75. Then your first unit costs you $7.75 to produce, your second also costs you $7.75, and so on. If you produce 5 units and your production cost per unit is $7.75, your total production cost is $38.75 (since 5 times 7.75 equals 38.75).

In each Market stage, you will decide the **maximum number of units you wish to sell** in the current Market stage. You may choose to sell 0, 1, 2, 3, 4, 5, 6, 7, or 8 units.

Choosing, say, 7 units as your maximum quantity to sell does not guarantee that you will sell 7 units. The process that determines how many units you actually sell is described later.

If you select 7 as your maximum number to sell but you only sell 3 units your total production cost will be for 3 and not 7 units. Think of units as being “made to order.” You choose the maximum number of units you are willing to sell, but you only produce the number of units you end up selling.

In addition to submitting a maximum number of units to sell, you will also submit a **price**. This price is the price that you are willing to sell *all* of your units for. You cannot sell different units for different prices. Prices can be any two decimal number from your cost of producing units to $20.00. The computer will not let you sell units at a loss.

Example: Say you select a maximum number of units to sell of 2 and a price of $8.00. If you end up selling both units you will sell them each for $8.00.

You are in a market with three other sellers. They are currently reading the same instructions you are and will be confronting the same decisions that you will. They will also be selecting a maximum number of units to sell and a price in each Market stage.

**What determines how many units you sell?** Once you and the other sellers have entered prices, all of your prices will be publicly displayed. You will see the prices they chose and they will see the price you chose. However, you will not know what maximum quantity they selected and they will not know what maximum quantity you selected.

The buyers in this experiment are computerized. Each buyer has some $ value for 1 unit. We refer to this value as their **buyer value**.

**If you post a price that is lower than the prices posted by all the other sellers in your market**, buyers will “line up” to purchase from you first. They will line up in descending order of their buyer value. In other words, the buyer with the highest buyer value will be “at the front of the line” and the buyer with the lowest buyer value will be at the back of the line.

**Remember: You cannot sell more units than the maximum number of units you select!**

Example: Say there are 2 buyers: Buyer 1 with a buyer value of $10.00 and Buyer 2 with a buyer value of $5.00. If you post a price of $8.00 and the other sellers post a price of $9.00, the buyers come to you first since your price is the lowest. Buyer 1 values a unit at $10.00 and you are selling units at $8.00, so Buyer 1 is willing to purchase 1 unit from you. Buyer 2 is next in line, but since he only values units at $5.00, he does not buy a unit from you.

Example: Say there are buyers with buyer values of $10.00, $9.00, and $8.00. Say you post a price of $7.80 and a maximum quantity of 2. Suppose that the other sellers in your market post prices of $7.95, $8.00 and $8.10. Since you have the lowest price, the buyers come to you first. All three buyers would like to buy a unit each from you since your price is lower than each of their buyer values. However, only the buyers with buyer values of $10.00 and $9.00 are able to buy from you since you set your maximum quantity to 2.

**If you post a higher price than another seller in your market**, you must wait until they have sold their maximum quantity. If they have sold their maximum quantity and there are still buyers who wish to buy at your price, these buyers will buy from you.

**If you and another seller in your market post identical prices**, the computer determines the number of buyers who wish to buy units at your common price. If there are “extra” units that cannot be divided evenly among the sellers who submitted the same price, the “extra” unit(s) is (are) randomly awarded by the computer.

Example: Say you and another seller both post a price of $8.25 and that 7 buyers are willing to buy units at that price. You and the other seller each sell 3 units and the 7th or “extra” unit is randomly assigned to either you or the other seller. You and the other seller each have a 50/50 chance of selling the extra unit.

### Summary of How Units Are Sold

**If your price is lower:**

You sell until you have sold your maximum quantity, or

You sell until your price is greater than any remaining buyer’s buyer value

**If your price is higher:**

You wait until any other sellers (with lower prices) have sold their maximum quantity, then the process is the same as above

**If your price is the same:**

The computer calculates the number of buyers who wish to buy at your common price. If there are “extra” units that cannot be divided evenly among the sellers who submitted the same price, the computer will randomly determine how to allocate the extra units.

*You can never sell more units than the maximum number of units you select!*

### Innovation Stage

You and the other sellers in your market will begin each block with the same production cost per unit: **$7.75 per unit**. However, in the Innovation stage you and the other sellers will each independently make choices which may allow your *own* production costs to be reduced. Your choices in the Innovation stage can only influence *your own* production costs and not those of the other sellers, and vice versa.

Your costs will be influenced by a **random process**. This process involves ten numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. Each of these numbers is equally likely to be selected by the process. In other words, the probability of any one number, say 6, being selected by the process is 1/10 or 10 %.

The process just described has two outcomes: **success** and **failure**. Success occurs when the process selects the number 10; failure occurs when the process selects any number other than 10 (numbers 1–9). Since the probability that the process will select the number 10 is 1/10 or 10 %, **the probability that the process results in success is 1/10 or 10 %**.

**If the process is a success**, your costs of producing units in the current and all future periods within a block will be reduced by **$0.25**.

Example: If you are successful in the Innovation stage of block 1, period 1, your cost of producing units is lowered from $7.75 to $7.50 for period 1 and all the remaining periods (2–10) in block 1.

**Note that your profits may be influenced by having lower production costs.**

During each Innovation stage, you will be asked to select the number of innovation processes you wish to undertake in the current period. In the first period you may choose any number of processes between 0 and 30. While you can choose up to 30 processes, **you may only receive one $0.25 cost reduction per period**.

Example: Say you attempt 11 processes. Suppose that the first 7 result in failure, but that the 8th process is a success (the number 10 is randomly selected). Then you will receive a cost reduction for the period. Because you can only have one cost reduction per period, the 9th, 10th and 11th processes are immaterial and will not be displayed.

It is important to note that even if you choose a large number of processes, success is not guaranteed because each process is randomly and independently determined.

The potential benefit of choosing at least one process is the chance of getting a cost reduction. However, **innovation processes are not costless**. Each process costs **$0.10**. So for every $0.10 you agree to spend, you have a 10 % chance of receiving a cost reduction of $0.25.

Note that you and the other sellers in your market make independent process decisions in each Innovation stage.

Example: Say you chose 6 processes and one of the other sellers chose 16. You spend $0.60 and the other seller spends $1.60, yet random chance may mean that you are successful and that the other seller is not because the computer picks different random outcomes for you both.

After each Innovation stage, you will learn how much the other sellers in your market spent on innovation processes and they will learn how much you spent. You will also learn whether the other sellers were successful or not, and vice versa.

### Profit

Your profit for a particular period is calculated as follows:

Notice that your profit *increases* in your price and in the number of units you sell. Your profit also *increases* with *decreases* in your production cost. Finally, your profit *decreases* (by $0.10) with each innovation process you buy.

The computer will calculate your profit for you. After each Market stage you will receive feedback about your profit. You *will not* receive information about the profit of the other sellers in your market, nor will they receive any feedback about your profit.

At the end of each period your profit (calculated according to the above formula) is added to the profit you have previously earned. The result is referred to as your **total profit**.

If your total profit dips below $0.00, the computer will not let you lose additional money. However, if you have $0.00 in total profit you will not be able to purchase any processes in the Innovation stage.

After each block, your total profit will reset. However, *you will be paid your earnings for all 3 blocks* at the conclusion of the experiment!

### Additional Instructions

Between blocks, your cost of producing units “resets” to $7.75 per unit.

Example: Say you had four successes in block 1, so that your cost of producing units was $6.75. At the conclusion of block 1, period 10, but before the start of block 2, period 1, your cost of producing units will reset to $7.75.

There are two types of blocks in this experiment: **single blocks** and **multiple blocks**.

Buyers have the same buyer values regardless of block type and they will only ever buy *at most one* unit from each seller.

In single blocks, each buyer demands one unit total; in multiple blocks, each buyer demands more than one unit total.

Again, even in multiple blocks where buyers demand more than one unit total, they will only buy *at most* one unit from each seller.

You will not be told whether you are playing in a single block or a multiple block.

Prior to the start of each block, you will be given an **endowment of $5.00**. This endowment is provided to allow you to buy innovation processes in the first period of the block if you so choose. You are under no obligation to buy processes in the first nor in any subsequent period. Your profits may be influenced by having lower production costs. If you wish, you can go the entire experiment without buying an innovation process. If you do so, your endowments will be part of your earnings paid to you at the experiment’s conclusion.

You will remain in the same market throughout the experiment. Thus, the other sellers in your market in block 1 will be the other sellers in your market in subsequent blocks as well.

### Review

In Innovation stages you choose a number of processes. Each process has a 1/10 or 10 % chance of success. Processes cost $0.10. Success means a $0.25 per unit cost reduction for the current and all future periods within a block.

In Market stages you choose a price and a maximum quantity. Buyers will buy from you first if your price is less than the other seller’s prices. Whether your price is initially the lowest or not, it must be less than their buyer value for them to purchase.

In single blocks, buyers only demand one unit total; in multiple blocks they demand more than one unit total. Regardless of block type, buyers buy at most one unit from each seller. You will not be told whether the block type is single or multiple.

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### Cite this article

Smyth, A. Competition, Cost Innovation, and X-inefficiency in Experimental Markets.
*Rev Ind Organ* **48, **307–331 (2016). https://doi.org/10.1007/s11151-015-9487-7

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### Keywords

- X-inefficiency
- Cost innovation
- Experimental economics